A gear reduction unit uses the countershaft shown in the figure. Gear A receives

power from another gear with the transmitted force $F_A$ applied at the $20$ pressure

angle as shown. The power is transmitted through the shaft and delivered through

gear $B$ through a transmitted force $F_B$ at the pressure angle shown.

Given: $F_A=250lbf,$ diameter of gear $A=12in,$ and diameter of gear $B=4\mathrm{.}8in.$

I. Determine the force $F_B,$ assuming the shaft is running at a constant speed $($static

equilibrium, i$.$e$.$ no acceleration$).$ Hint: Use moment equilibrium equation about the $x-$

axis. $(5$ points$)$

II$.$ Find the bearing reaction forces, assuming the bearings act as simple supports. Hint:

Find $Cy,Cz,Oy,Oz.$ There are no support reactions in the $x-$direction! $(10$ points$)$

III. Draw shear$-$force and bending$-$moment diagrams for the shaft. Make one set for

the horizontal plane and another set for the vertical plane. Indicate at what point does

the maximum bending moment occur $($point $O,A,C,$ or $B)?(10$ points$)$

IV$.$ Determine the point of maximum bending moment. $(5$ points$)$